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Example 4: The daily wages (in `) of 10 workers of a factory are given as:

1432, 1441, 1528, 1554, 1435, 1526, 1323, 1333, 1438, 1440
Answer the following questions.
(a) What is the minimum wage?

(b) What is the maximum wage?
(c) What is the range of the daily wages of the workers?

Solution: Arranging the daily wages (in `) of 10 workers in ascending order, we get
1323, 1333, 1432, 1435, 1438, 1440, 1441, 1526, 1528, 1554
(a) The minimum wage is `1323.
(b) The maximum wage is `1554.

(c) The range of the wages = `1554 – `1323 = `231

Representative Values of Data

A numerical value that represents a generalised picture of the data is known as the representative
value of the data. It is also known as a measure of the central tendency of data.

It is a single value that reflects the average value, i.e., it is the approximate middle value of a set of
data. There are three common representative values, namely, mean (arithmetic mean), median,
and mode.

Arithmetic Mean or Mean

The arithmetic mean or mean is an average of group of observations.

Sum of all observations
Arithmetic mean or Mean or Average (A.M.) =
Number of observations

The arithmetic mean of n observations x , x , x , x , x , …., x is given by
n
4
5
3
1
2
x + x + x + ... + x ∑ x
A.M. = 1 2 3 n =
n n
where Sx shows the sum of the observations The symbol S is called ‘summation
or sigma’ and is used for word
Sx = x + x + x + x + x + …. + x n ‘the sum of ’.
3
4
5
1
2
We can also represent arithmetic mean by x .
Example 5: Find the arithmetic mean of the following observations.
14, 21, 48, 27, 14, 10, 49, 21, 23, 29
Solution: Total number of observations = 10
Sum of the observations = 14 + 21 + 48 + 27 + 14 + 10 + 49 + 21 + 23 + 29 = 256
We have,

Sum of all observations
Arithmetic mean (A.M.) = For finding mean, it is not
Number of observations Note: necessary to arrange the given

256 observations in ascending or
x = = 25.6 descending order.
10

Mathematics-7 310